NEW YORK — A photograph begins in fakery (the act of rendering three dimensions as two) and ends in fact (the physical object that is negative or print). Technology has made the situation even more complicated, since now the fact isn’t likely to be physical, unless you think pixels on a screen qualify.

So a tension between false and real has always defined photography, a tension that has become that much more intriguing in this digital age. Two new shows at the Metropolitan Museum of Art, “Faking It: Manipulated Photography Before Photoshop” and “After Photoshop: Manipulated Photography in the Digital Age,” look at this tension past and present. They run through Jan. 27 and May 27, respectively.

Exhibition names don’t come any more cheerfully candid than “Faking It.” It’s the first major survey of its kind. The earliest of the show’s 200-odd photographs (and some are very odd) dates to 1851, the latest to 1987.

Some instances of manipulation announce themselves as such: 19th-century colorization, a giant ear of corn, or a Bill Brandt nude where the model has three arms. Only trickery could account for Maurice Guibert’s marvelous 1892 portrait of Henri de Toulouse-Lautrec, which shows the painter at his easel sitting across from himself, posing for his own self-portrait. Wanda Wulz’s “Io + Gatto [Cat + I]” unnervingly overlays the photographer’s face with that of her cat. The resulting image is a complete fiction, yes, but it gets at a higher truth about the relationship between human and animal that no “straight” photograph ever could.

Wulz’s photograph also stands as a classic example of why the Surrealists adored photography, with the wondrous effects that could be produced in the darkroom. Yves Klein, no Surrealist but one of their cheerier legatees, offered another example with his “Leap Into the Void,” which famously shows him seemingly diving out of a second-story window. It’s the product of two different negatives, of course. At some level, we know it’s pure artifice — yet that sense of liberation and cartoonish, Road Runner-style defying of physical law is a fantasy we want to embrace as reality.

Other instances of camera fakery predicate themselves on evading detection, either for aesthetic or political reasons.

A limitation of early photography was that the sky tended to be overexposed. So to get clouds to register in his seascapes, Gustave Le Gray would print from two negatives. Carleton Watkins would do the same for a landscape. Conversely, Edouard Baldus
painted in
the clouds in his “Boats at Low Tide, Boulogne,” from 1855. What was real on the negative would have looked unreal on the print. Le Gray, Watkins, and Baldus were improving upon imperfection — adding to the print what the negative could not provide. Then there’s something like Oscar Gustav Rejlander’s “Two Ways of Life,” in which the photographer employed more than 30 negatives to achieve his desired effect.

Revision in writing is a good thing. Alteration in painting is a given. But crediting photography with a veracity we don’t assume other media possess, we assume dishonesty when manipulation occurs. But is aesthetic ambition — a striving to eliminate imperfection — a bad thing? “The minute you pick up a camera you begin to lie — or tell your own truth,” Richard Avedon once said. “It’s just a matter of how far you choose to go.”

A different kind of imperfection confronted propagandists — and a very different imperative motivated them. As policies changed, photographic fakery could be employed to change past events (or at least change their recorded appearance). The Soviet Union, where photographic manipulation qualified as a tool of state policy, has a special chapter in any history of camera fakery. (Not that capitalism hasn’t employed it, too — as a form of economic policy, commonly referred to as advertising.)

“Faking It” includes a 1949 print of a picture taken in 1922. It shows Stalin and Lenin sitting together, looking amiable and cooperative. You’d never know to look at it that Stalin’s complexion has been retouched or that he’s been made to look more prominent in the photograph so that he, not Lenin, is the dominant figure. Even more telling are four versions of a photograph taken in 1926. In the first, Stalin stands with four political associates. Each successive image shows one fewer comrade, until just one remains. He’s Sergei Kirov, who unlike the others was never purged. He was never purged because he was safely dead — assassinated, and likely at Stalin’s behest!

“Faking It” includes the work of some famous photographers: Watkins, Avedon (if fashion photography doesn’t fall under the heading of fakery, what does?), Brandt, Weegee (making Lyndon Johnson look like Pinocchio), Edward Steichen, Duane Michals (of course, with his multiple-image fictions). But “Faking It” is a show about style and (especially) technique, not individual sensibilities. Unknown Artist is the most common name in the show. Ultimately, it’s about the medium and how to some degree it has always seemed like a form of magic. Practitioners of magic are known as magicians, and what are magicians minus their tricks?

Thanks to the computer, the tricks have gone high tech. The manipulation’s still there, it’s just sleeker — and with vastly greater possibilities. “After Photoshop” offers some three dozen examples. Using the computer lets Filip Dujardin, who once wanted to be an architect, “show” in two realistic-seeming dimensions the buildings he envisions in three highly imaginary dimensions (the dimensions are real, of course, it’s the buildings that aren’t). In “110 Junction,” Matthew Porter uses the computer to put a ’70s muscle car high above a city street, like a still from a Steve McQueen movie that never was but ought to have been.

All art is a form of fabrication, in both senses of the word: something concocted, a kind of falsehood; and something made, a piece of handiwork. In ways that are both bracing and chastening, “Faking It” and “After Photoshop” remind us that even as the old questions about the relationship between those two senses refuse to be settled — what is real? what is true? there is a difference, right? — the ways to consider them keep changing.